An upper limit calculator (UL-CALC) for undetected extended sources with radio interferometers: radio halo upper limits

Radio halos are diffuse, extended sources of radio emission detected primarily in massive, merging galaxy clusters. In smaller and/or relaxed clusters, where no halos are detected, one can instead place upper limits to a possible radio emission. Detections and upper limits are both crucial to constrain theoretical models for the generation of radio halos. The upper limits are model dependent for radio interferometers and thus the process of obtaining these is tedious to perform manually. In this paper, we present a Python based tool to automate this process of estimating the upper limits. The tool allows users to create radio halos with defined parameters like physical size, redshift and brightness model. A family of radio halo models with a range of flux densities, decided based on the rms noise of the image, is then injected into the parent visibility file and imaged. The halo injected image and the original image are then compared to check for the radio halo detection using a threshold on the detected excess flux density. Injections separated by finer differences in the flux densities are carried out once the coarse range where the upper limit is likely to be located has been identified. The code recommends an upper limit and provides a range of images for manual inspection. The user may then decide on the upper limit. We discuss the advantages and limitations of this tool. A wider usage of this tool in the context of the ongoing and upcoming all sky surveys with the LOFAR and SKA is proposed with the aim of constraining the physics of radio halo formation. The tool is publicly available at https://github.com/lijotgeorge/UL-CALC.